Continuous wave (cw) radar system for phase-coded time delayed transmit-receive leakage cancellation

ABSTRACT

Disclosed is a method, system, and apparatus for transmitting a randomly phase-coded CW waveform in a manner that suppresses signal leakage and enables the recovery of polyphase subcodes advantageous for the purposes of correlation and pulse compression. The CW system transmits and receives a random waveform while concurrently providing properly delayed phase conversion parameters (ϕ i −θ i ) from a corrections generator to various range gates. Each range gate processes any echo returns using a most recent phase conversion parameters (ϕ k −θ k ) provided and correlation of the resulting echo subcodes ϕ R  produce either target indications or noise signals, depending on the most recent phase conversion parameters (ϕ k −θ k ) provided to the range gate. The system may transmit the randomly phase-coded CW waveform while recovering any phase code {ϕ 1 , ϕ 2 , . . . ϕ N } that lends itself to advantageous pulse compressions.

RELATION TO OTHER APPLICATIONS

This patent application claims the benefit of U.S. Provisional Application No. 62/479,381 filed Mar. 31, 2016, which is hereby incorporated in its entirety.

FIELD OF THE INVENTION

One or more embodiments relates generally to a randomly phase-coded continuous wave (CW) radar system.

BACKGROUND

Random signal radars are radars whose transmitting signal is typically modulated by some noise source in order to generate a random transmitting signal. Because of the random properties of the signal, these radars have multiple advantages compared with conventional radars, including unambiguous measurement of range and Doppler estimations, high immunity to noise, lower detection probabilities, and advantageous ambiguity functions, among others.

For most applications, the random signal is either transmitted directly from the noise-generating source or generated digitally, then converted to analog and upconverted to carrier level. Correlation of the echo returns uses the principle that when the delayed replica of the transmitted signal is correlated with the actual target echo, the peak value of the correlation process can indicate the distance to the target. The replica of the transmitted noise, delayed, is correlated with a received signal, and strong correlation peaks are utilized to provide round trip time (RTT) estimations and ranging. This methodology generally requires a significant amount of processing and computational resources at both the transmitting and receiving ends of the system, and challenges abound. Additionally, because correlations are conducted using the delayed replica of the random transmission as a template, any ability to utilize specific phase codes more amenable to advantageous phase compressions is generally sacrificed.

Additionally in CW systems random or otherwise, leakage from a transmitted signal generally occurs due to circuit leakages, free space propagation, near field coupling, or other propagation modes. The details depend on the specific system architecture and whether single or multiple antennas are used. For close in targets, the leakage signal strength s_(l)(t) is generally much smaller than the signal strength returned to the radar from the target, however at longer ranges or for low radar cross section targets, the received signal from the target s_(t)(t) is very weak. Since the receiver must operate when transmission is occurring, the leakage signal can still be much larger than the target return. In the absence of close-in clutter the leakage can be reduced by increasing the antenna spacing, but there is a practical limit to this. In the actual construction and operation of a radar system it is impossible to achieve zero leakage. Thus the isolation between the transmitting and receiving antennas (or channels) is often one of the limiting factors in the performance of CW radars.

It would be advantageous to provide a CW radar system which employs a randomly phase-coded system in order to realize the associated advantages while also providing the ability to recover specific phase codings more amenable to advantageous phase compressions. It would be additionally advantageous if the CW system eliminated some portion of the significant processing and computational resources associated with delayed replica correlation. It would provide additional advantage is such a system could transmit continuous wave signal in a manner greatly mitigating the impact of signal leakage.

These and other objects, aspects, and advantages of the present disclosure will become better understood with reference to the accompanying description and claims.

SUMMARY

A particular embodiment of the Continuous Wave (CW) Radar System comprises a random waveform generator providing a plurality of random subcodes θ_(i). The random waveform generator communicates the random subcodes θ_(i) to a modulator, which upconverts the random subcode θ_(i) to a modulated subcode θ′_(i) for subsequent transmission. The modulated subcode θ′_(i) generated is an electromagnetic signal having a frequency and a phase over a subpulse width τ, where the frequency is typically fixed and the phase is dependent on the most recent random subcode θ_(i) received. The modulator communicates the modulated subcode θ′_(i) to a transmitting antenna as well as to a corrections generator.

In conjunction, a polyphase subcode generator produces a polyphase subcode ϕ_(i) corresponding to each random subcode θ_(i), The polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having at least N number of members. For example, the polyphase subcode ϕ_(i) may be a member of a set defining one of the code sequences known as Barker, Frank, Chu, Milewski, and others, however this is not required, and the polyphase subcode ϕ_(i) may be a member of any set defining any phase-coding scheme. The polyphase subcode generator additionally communicates the polyphase subcode ϕ_(i) to the corrections generator. The corrections generator is further in data communication with a plurality of range gates RG_(j), where j is used to denote a counting integer greater than or equal to 1 and less than some maximum integer m. Each range gate RG_(j) provides range binning for a range interval of the CW system.

Generally for each subpulse width τ, the corrections generator generates a phase conversion parameter (ϕ_(i)−θ_(i)) using the subcode θ_(i) and the corresponding polyphase subcode ϕ_(i) received. The corrections generator subsequently provides the phase conversion parameter (ϕ_(i)−θ_(i)) generated for the random subcode θ_(i) to each individual range gate RG_(j) using a delay D_(j) specific and unique to that particular range gate. In a typical embodiment, each individual range gate RG_(j) has an associated delay generally dependent on a time equal to (τ×j)+ΔT_(P(j)), where j corresponds to the indexing integer of the range gate, (τ×j) indicates the subpulse width τ multiplied by the indexing integer of the range gate RG_(j), and ΔT_(P(j)) is a processing time required by receiving components in the system. Under this arrangement, each range gate RG_(j) generally receives a new phase conversion parameter (ϕ_(i)−θ_(i)) corresponding to each subpulse width τ of the modulated subcode θ′_(i) transmitted. However, because of the delay D of (τ×j)+ΔT_(P(j)) applicable to each range gate RG_(j), the phase conversion parameter most recently received at a given range gate from corrections generator varies among the range gates. As a result, each range gate RG_(j) has a most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from the corrections generator.

The CW system receives and processes echoes by receiving a modulated echo θ′_(R) and demodulating the echo to generate a demodulated subcode θ_(R). The demodulated subcode θ_(R) is provided to each range gate RG_(j), which converts the phase of the demodulated subcode θ_(R) using its most recent phase conversion parameter (ϕ_(k)−θ_(k)). The range gate RG_(j) adds the resulting echo subcode ϕ_(R) to a string of subcodes and then correlates the updated polyphase sequence against the set of N polyphase subcodes utilized by the polyphase subcode generator. As a result of the associated time delays generating different (ϕ_(k)−θ_(k)) parameters to each range gate, and the random nature of the modulated subcode θ′_(i) being transmitted, and the demodulated subcode θ_(R) being supplied, the resulting phase conversion and correlation at each range gate substantially generates either a compressed {ϕ₁, ϕ₂, . . . ϕ_(N)} pulse when the echo originates within the range interval corresponding to the range gate RG_(j), or substantially generates a noise signal otherwise. Subsequent integration is typically utilized to identify the range interval from which a given modulated echo θ′_(R) originated.

The novel apparatus and principles of operation are further discussed in the following description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an embodiment of the CW system.

FIG. 2 illustrates a specific embodiment of a range gate.

FIG. 3 illustrates a plurality of random phase subcodes.

FIG. 4 illustrates a modulated randomly phase-coded waveform.

FIG. 5 illustrates a plurality of polyphase subcodes.

FIG. 6 illustrates another embodiment of the CW system.

FIG. 7 illustrates exemplary parameters utilized by the CW system.

FIG. 8 illustrates delayed phase conversion parameters (ϕ_(i)−θ_(i)) provided to a plurality of range gates.

FIG. 9 illustrates a response of the plurality of range gates to echo returns from a first object.

FIG. 10 illustrates a response of the plurality of range gates to echo returns from a second object.

FIG. 11 illustrates a response of the plurality of range gates to echo returns from multiple objects.

FIG. 12 illustrates a response of the plurality of range gates to echo returns from an objects in the presence of signal leakage.

Embodiments in accordance with the invention are further described herein with reference to the drawings.

DETAILED DESCRIPTION OF THE INVENTION

The following description is provided to enable any person skilled in the art to use the invention and sets forth the best mode contemplated by the inventor for carrying out the invention. Various modifications, however, will remain readily apparent to those skilled in the art, since the principles of the present invention are defined herein specifically to provide a method, system, and apparatus for transmission of a random phase-coded waveform while providing for recovery of an underlying phase code.

Provided here is a method, system, and apparatus for transmitting a randomly phase-coded CW waveform in a manner enabling the recovery of polyphase subcodes advantageous for the purposes of correlation and pulse compression. The CW system disclosed transmits and receives a random phase-coded waveform while concurrently providing properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) from a corrections generator to each of a plurality of range gates RG_(j). Each range gate identifies and processes any echo returns using a most recent phase conversion parameters (ϕ_(k)−θ_(k)) provided from the corrections generator, and correlation of the resulting echo subcodes ϕ_(R) produce either target indications or noise signals, depending on the most recent phase conversion parameters (ϕ_(k)−θ_(k)) provided to the range gate. The method, system, and apparatus provided differs substantially from that employed by typical random radars transmitting randomly phase coded CW waveforms, which typically rely on recording and updating a series of echo subcodes received for subsequent comparison against a delayed replica, in order to determine round trip time (RTT) and provide ranging functionality. Additionally, in typical random radars, the random transmitted waveform is typically correlated against the (also random) delayed replica, and any ability to utilize specifically advantageous phase codes is lost. In contrast, the system, method, and apparatus disclosed here provides for transmission of a random CW waveform while also allowing the use of any phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} that lends itself to advantageous pulse compressions.

A particular embodiment of the Continuous Wave (CW) Radar System disclosed is illustrated at FIG. 1. At FIG. 1, CW System 100 comprises random waveform generator 101 typically comprising a noise source 102. Random waveform generator 101 generates a random phase coded waveform based on noise source 102, where the random phase coded waveform comprises a plurality of random subcodes θ_(i) with each random subcode θ_(i) corresponding to a subpulse width τ, where τ is a measure of time. The random waveform generator 101 communicates the random subcode θ_(i) to a modulator 103 which receives each random subcode θ_(i) and upconverts the random subcode θ_(i) to a modulated subcode θ′_(i). In some embodiments modulator 103 comprises a digital processor and provides a digital-to-analog conversion of the random subcode θ_(i) in order to upconvert to the modulated subcode θ′_(i). Such digital modulation methods are known in the art. The modulated subcode θ′_(i) generated is an electromagnetic signal having a frequency and a phase over the subpulse width τ, where the frequency is typically fixed and the phase is dependent on the random subcode θ_(i) corresponding to a subpulse width τ. In particular embodiments, this is the most recent random subcode θ_(i) received by Modulator 103. The modulator communicates the modulated subcode θ′_(i) to a transmitting antenna 104, which transmits the modulated subcode θ′_(i) at a time t_(i) for a period of time equivalent to the subpulse width τ. Random waveform generator 101 additionally communicates each random subcode θ_(i) to corrections generator 106 via, for example, 107.

In conjunction, a polyphase subcode generator 105 produces a polyphase subcode corresponding to each random subcode θ_(i). The polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having N number of members. For example, the polyphase subcode ϕ_(i) may be a member of a set defining one of the code sequences known as Barker, Frank, Chu, Milewski, and others, however this is not required. Within this disclosure, the polyphase subcode ϕ_(i) may be a member of any set defining any phase-coding scheme. Polyphase subcode generator 105 additionally communicates the polyphase subcode ϕ_(i) to corrections generator 106, as illustrated.

Corrections generator 106 is in data communication with a plurality of range gates RG_(j), where j is used to denote a counting integer greater than or equal to 1 and less than some maximum integer m, where m>1. For example at FIG. 1, the plurality of range gates RG_(j) comprises RG₁, RG₂, RG₃, and so on to the range gate indicated as RG_(m). Each range gate RG_(j) generally corresponds to a range bin dependent on the subpulse width τ utilized, as is typical for CW radars. For example at FIG. 1, range gate RG₁ provides binning for the range interval generally indicated by RH₁, range gate RG₂ provides binning for the range interval generally indicated by RH₂, range gate RG₃ provides binning for the range interval generally indicated by RH₃, and range gate RG_(m) provides binning for the range interval generally indicated by RH_(m). In typical embodiments, each range interval generally covers a physical displacement equal to about τc/2, where c is the speed of light. As indicated at FIG. 1 and as will be discussed later, in typical embodiments there is no RG_(j) range gate intended to provide binning for the range interval RH₀ in order to enhance leakage suppression.

As discussed, for each subpulse width τ associated with a random subcode θ_(i), corrections generator 106 receives both the random subcode θ_(i) generated by random waveform generator 101 and the polyphase subcode ϕ_(i) generated by polyphase subcode generator 105. Corrections generator 106 then generates a phase conversion parameter (ϕ_(i)−θ_(i)) using the subcode θ_(i) and the corresponding polyphase subcode ϕ_(i). Corrections generator 106 subsequently provides the phase conversion parameter (ϕ_(i)−θ_(i)) generated for the random subcode θ_(i) and corresponding polyphase subcode ϕ_(i) to each individual range gate RG_(j) using a delay D_(j) specific and unique to that particular range gate, where the delay D_(j) follows the time t_(i) when transmitting antenna 104 transmits the modulated subcode θ′_(i) derived from the random subcode θ_(i). These delays are represented at FIG. 1 by the series of delays illustrated as D₁, D₂, D₃, and D_(m). In a typical embodiment the individual delays D_(j) are representative of time periods defined generally by (τ×j)+ΔT_(P(j)), where τ is the subpulse width τ and ΔT_(P(j)) is typically a time period required in order to receive and process an echo to a form suitable for delivery to the plurality of range gates RG_(j), as will be discussed. The ΔT_(P(j)) may be a period specific and known by CW system 100 for each range gate RG_(j) based on timing diagnostics or other testing, or in some embodiments may be a period common to all range gates RG_(j) in the plurality. However, the individual delays D_(j) need not adhere or strictly depend on the exemplary (τ×j)+ΔT_(P(j)) expression, provided the individual delays D_(j) are specific and unique to a range gate RH_(j). In some embodiments, a timing circuit 110 is in communication with at least random waveform generator 101, polyphase subcode generator 105, and corrections generator 106, in order to provide timing signals for appropriate random subcode θ_(i) and polyphase subcode ϕ_(i) delivery, association for generating the phase conversion parameter (ϕ_(i)−θ_(i)), and to provide timing or other signals by which a given phase conversion parameter (ϕ_(i)−θ_(i)) is provided to a given range gate RG_(j) based on an appropriate delay D_(j), among other synchronizations that may be necessary.

The phase conversion parameter (ϕ_(i)−θ_(i)) is generated by corrections generator 106 using an operation such as a digital process, an analog process, or some combination therein. The phase conversion parameter (ϕ_(i)−θ_(i)) generated by the digital process, the analog process, or the combination can be used in conjunction with a given random subcode θ_(i) to substantially produce the polyphase subcode ϕ_(i) produced by polyphase generator 105 which corresponds to the given random subcode θ_(i). As previously mentioned, polyphase subcode generator 105 produces a polyphase subcode ϕ_(i) corresponding to each random subcode θ_(i) generated by random waveform generator 101 for each subpulse width τ, and corrections generator 106 then generates a phase conversion parameter (ϕ_(i)−θ_(i)) using the subcode θ_(i) and the corresponding polyphase subcode ϕ_(i), such that for a specific random subcode θ_(i(S)) and a corresponding specific polyphase subcode ϕ_(i(S)), corrections generator 106 generates a specific phase conversion parameter (ϕ_(i(S))−θ_(i(S))). Given the random nature of the random subcodes θ_(i) generated by random waveform generator 101, in order to substantially produce the specific polyphase subcode ϕ_(i(S)) corresponding to the specific random subcode θ_(i(S)) using a phase conversion parameter, both the specific phase conversion parameter (ϕ_(i(S))−θ_(i(S))) generated for the specific random subcode θ_(i(S)) and an approximate version or replica of the specific random subcode θ_(i(S)) must be present, as discussed further below.

Under this arrangement, each range gate RG_(j) generally receives a new phase conversion parameter (ϕ_(i)−θ_(i)) corresponding to each subpulse width τ of the modulated subcode θ′_(i) transmitted by transmitting antenna 104. However, because of the delay D of, for example, (τ×j)+ΔT_(P(j)) applicable to each range gate RG_(j), the phase conversion parameter most recently received at a given range gate from corrections generator 106 varies among the range gates. As a result, each range gate RG_(j) has a most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from corrections generator 106, where the (ϕ_(k)−θ_(k)) received is a properly delayed phase conversion parameter (ϕ_(i)−θ_(i)), and where generally at any given instant, the most recent phase conversion parameter (ϕ_(k)−θ_(k)) for a specific range gate RG_(j) is unique to the specific range gate RG_(j) in the plurality of range gates RG_(j). For example at FIG. 1, the most recent phase conversion parameter (ϕ_(k)−θ_(k)) for RG₁ is (ϕ_(k(1))−θ_(k(1))), the most recent phase conversion parameter (ϕ_(k)−θ_(k)) for RG₂ is (ϕ_(k(2))−θ_(k(2))), and the most recent phase conversion parameter (ϕ_(k)−θ_(k)) for RG₃ is (ϕ_(k(3))−θ_(k(3))), with typically (ϕ_(k(1))−θ_(k(1))), (ϕ_(k(2))−θ_(k(2))), and (ϕ_(k(3))−θ_(k(3))) representing non-equivalent signals due at least to the random nature of the random subcodes θ_(k(1)), θ_(k(2)), and θ_(k(3)) on which the respective most recent phase parameters are based, as well as the respective polyphase subcodes ϕ_(k(1)), ϕ_(k(2)), and ϕ_(k(3)) which typically vary from a first subpulse width τ to a subsequent subpulse width τ.

CW system 100 performs the steps described on a cyclic basis, in order to transmit a continuous wave random radar signal comprising a plurality of modulated subcodes θ′_(i) and, for each modulated subcode θ′_(i), provide phase conversion parameters (ϕ_(i)−θ_(i)) to each range gate RG_(j), where the phase conversion parameter (ϕ_(i)−θ_(i)) comprises a polyphase subcode ϕ_(i) corresponding to one of the transmitted modulated subcodes θ′_(i), and where the polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having at least N number of members. Each of the range gates RG_(j), utilizes the phase conversion parameters (ϕ_(i)−θ_(i)) received in order to process a received echo, as discussed below.

CW system 100 receives and processes echoes by receiving a modulated echo θ′_(R) through antenna 108 and communicating the modulated echo θ′_(R) to demodulator 109, which demodulates the echo, generates a demodulated subcode θ_(R), and provides the demodulated subcode θ_(R) to each range gate RG_(j) over the processing time ΔT_(P(j)). The processing period ΔT_(P(j)) is generally the period from receipt of an echo at a receiving antenna such as antenna 108 through supply of the demodulated subcode θ_(R) to a specific range gates RG_(j), and as discussed may be a time period common to all range gates RG_(j). In certain embodiments, the ΔT_(P(j)) is used to determine a delay D_(j) of (τ×j)+ΔT_(P(j)) observed by corrections generator 106. For a given CW system 100, the processing periods ΔT_(P(j)) with respect to a given demodulator 109 and a given range gate RG_(j) may be determined for a given collection of hardware components. In typical embodiments, timing circuit 110 is further in communication with demodulator 109 to provide timing signals for coordination among at least random waveform generator 101, polyphase subcode generator 105, and corrections generator 106. In particular embodiments demodulator 109 comprises a digital processor and provides an analog-to-digital conversion of the modulated echo θ′_(R) in order to demodulate the echo to the demodulated subcode θ_(R). Such digital demodulation methods are known in the art.

Having received the demodulated subcode θ_(R) from demodulator 109, each range gate RG_(j) converts the phase of the demodulated subcode θ_(R) using its most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from corrections generator 106 and generates an echo subcode ϕ_(R). The range gate RG_(j) adds the resulting echo subcode ϕ_(R) to a string of subcodes comprising echo subcodes previously received to generate an updated polyphase sequence, and then correlates the updated polyphase sequence using a matched filter, where in an embodiment the matched filter utilizes a reference register comprising the set of N polyphase subcodes utilized by polyphase subcode generator 106. As a result of the associated time delays generating different (ϕ_(k)−θ_(k)) parameters to each range gate, and the random nature of the modulated subcode θ′_(i) being transmitted and the demodulated subcode θ_(R) being supplied, as a given range gate phase rotates or converts the demodulated subcode θ_(R) for a given subpulse width τ to generate the updated polyphase sequence, the correlation of the updated polyphase sequence will generate a compressed {ϕ₁, ϕ₂, . . . ϕ_(N)} pulse only when the delayed (ϕ_(k)−θ_(k)) parameter matches an echo originating within the range interval corresponding to the range gate RG_(j), and substantially generate a noise signal otherwise. Subsequent integration of the output of each matched filter within the plurality of range gates RG_(j) is subsequently utilized to identify the range interval from which a given modulated echo θ′_(R) originated.

This methodology differs substantially from that employed by typical random radars transmitting randomly phase coded CW waveforms. In a typical random radar, following receipt of an echo analogous to modulated echo θ′_(R), the random radar records and updates a series of echo subcodes received, then compares the resulting string of subcodes to a delayed replica of previously transmitted subcodes in order to determine a round trip time (RTT), based on when the delayed replica was originally transmitted. The correct range gate is then generally activated based on the RTT resulting from this direct comparison of the received and replicated strings of subcodes. Further, any pulse compression which is performed is conducted using a matched filter having some version of the delayed replica as a template. Because the transmitted waveform is necessarily random and the delayed replica is subsequently also random, this eliminates any ability to generate phase codes which may be more amenable to phase compression, such as the aforementioned Barker, Frank, Chu, Milewski, and other phase code schemes. In contrast, CW system 100 of FIG. 1 transmits and receives a random waveform while avoiding the necessary use of a delayed replica for RTT determination, by providing properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) from corrections generator 106 to the various range gates RG_(j). In addition to avoiding the additional processing associated with the necessary storing and subsequent comparison against a delayed replica as performed in current random radars, the methodology of CW system 100 also has the significant advantage of enabling recovery of the underlying phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} associated with a given {θ₁, θ₂, . . . θ_(N)} series of modulated subcodes θ′_(i) transmitted, based on the phase conversion parameters (ϕ_(i)−θ_(i)) appropriately delayed and provided by corrections generator 106. This allows use of any phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} that lends itself to advantageous pulse compressions while concurrently transmitting a randomly phase-coded CW waveform.

The operation of CW system 100 is further discussed with reference to FIG. 2. FIG. 2 illustrates an embodiment of one of the plurality of range gates RG_(j) as range gate 211. Range gate 211 comprises a phase conversion module 212 receiving a most recent phase conversion parameter (ϕ_(k)−θ_(k)) from corrections generator 106 and a demodulated subcode θ_(R) from demodulator 109. Phase conversion module 212 converts the phase of the demodulated subcode θ_(R) using the most recent phase conversion parameter (ϕ_(k)−θ_(k)) and generates echo subcode ϕ_(R). Range gate 211 adds the resulting echo subcode ϕ_(R) to a string of subcodes {ϕ_(R(i-1)), ϕ_(R(i-2)), ϕ_(R(i-3)) . . . } previously received and held in, for example, shift register 213. At each receipt of new echo subcode ϕ_(R), range gate 211 correlates the string of subcodes using matched filter 214 having a reference register 215, with reference register 215 comprising the advantageous set of N polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)} utilized by polyphase subcode generator 105. Due to the 2τ(j)+ΔT_(P(j)) delay of the most recent phase conversion parameter (ϕ_(k)−θ_(k)) among the range gates RG_(j), the phase conversion operation will provide a string of subcodes {ϕ_(R(i-1)), ϕ_(R(i-2)), ϕ_(R(i-3)) . . . } closely mirroring the N polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)} only if range gate 211 corresponds to the range interval where a modulated echo θ′_(R) originated, and provide substantially noise otherwise. As a result, when range gate 211 corresponds to the range interval where the modulated echo θ′_(R) originated, matched filter 214 provides the advantageous pulse compression enabled by the N polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)}, and generally produces a noisy output otherwise. The compression of matched filter 214 is subsequently provided to integrator 216 and output 217. The phase conversion module 212 may generate an specific echo subcode ϕ_(R(S)) from a specific demodulated subcode θ_(R(S)) and a specific most recent phase conversion parameter (ϕ_(k)−θ_(k))_((S)) using an operation such as a digital process, an analog process, or some combination therein.

It is understood that although the N polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)} utilized for correlation as described above may comprise a set of N repeating polyphase subcodes, this is not required. In some embodiments, polyphase subcode generator 105 utilizes a non-repeating set of polyphase subcodes and corrections generator 106 acts to additionally provide each subcode ϕ_(i) comprising a phase conversion parameter (ϕ_(i)−θ_(i)) to each range gate with a delay similar to that utilized for the phase conversion parameter (ϕ_(i)−θ_(i)), in order that the range gate may update its matched filter template in a manner similar to updating the string of subcodes {ϕ_(R(i-1)), ϕ_(R(i-2)), ϕ_(R(i-3)) . . . }. However in certain embodiments, polyphase subcode generator 105 utilizes a set of N polyphase subcodes in a repeating sequential order, and in other embodiments, a matched filter comprising a range gate comprises a reference register, and the reference register comprises each of the polyphase subcodes arrayed in the sequential order.

It is additionally understood that the delays D such as D₁, D₂, D₃, . . . , D_(m) formulated as, for example, as (τ×j)+ΔT_(P(j)) may be explicit measures of time, or alternatively may be determined based on some database or other index b, where b is generated and updated based on each generation of a random subcode θ_(i) generally having the subpulse width τ, or based on transmission of a modulated subcode θ′_(i) generally having the subpulse width τ, or both. For example, when timing circuit 110 provides clocking signals to random waveform generator 101 and polyphase subcode generator 105 for the coordinated generation of the random subcode θ_(i), the polyphase subcode ϕ_(i), and supply of the respective subcodes to corrections generator 106, corrections generator 106 may generate a phase conversion parameter (ϕ_(i)−θ_(i))_(b) for storage in a database indexed by b. Similarly, in a synchronized operation, the time t_(i) corresponding to transmission of a given modulated subcode θ′_(i) may be associated with the index b. As a result, based on the clocking signals and the synchronization of timing circuit 110, index b itself may be utilized as a counter for the appropriate passage of time. In certain embodiments, CW system 100 may operate by providing phase conversion parameters to each range gate RG_(j) based on signals provided by timing circuit 110 and provide a phase conversion parameter (ϕ_(i)−θ_(i))_((b-j)) to each range gate RG_(j). For example, when the operations of CW system 100 are synchronized based on signals from timing circuit 110 and an index (b-0) is associated with a transmission time at a time t_(i), the timing circuit 110 may provide a signal directing corrections generator 106 to provide a phase conversion parameter (ϕ_(i)−θ_(i))_((b-1)) to RG₁, a phase conversion parameter (ϕ_(i)−θ_(i))_((b-2)) to RG₂, and phase conversion parameter (ϕ_(i)−θ_(i))_((b-m)) to a range gate RG_(m). CW system 100 may use any appropriate indexing scheme in order to track the provision of phase conversion parameters to specific range gates following appropriate delays.

An exemplary illustration of the random subcodes θ_(i) which might be generated by random waveform generator 101 is shown at FIG. 3, which depicts a plurality of subcodes θ_(i) extending over a time period with the time period divided into substantially equal subpulse widths τ. At FIG. 3, the plurality of random subcodes θ_(i) defines a phase value between 0 and 360 degrees. Random waveform generator 101 provides a random subcode θ_(i) between 0 and 360 at each τ, such as the random subcode θ₁ at a first τ, the random subcode θ₂ at a second τ, and so on. The phase values generated across the time period depicted are generally indicated by circles. Random waveform generator 101 communicates the random subcodes θ_(i) to modulator 103 and further to corrections generator 106, as discussed.

Modulator 103 receives the random subcodes θ_(i) and upconverts each random subcode θ_(i) to a modulated subcode θ′_(i). A plurality of modulated subcodes θ′_(i) generated by modulator 103 in response to a plurality of subcodes θ_(i) provided by random waveform generator 101 is illustrated at FIG. 4 as the phase-coded waveform generally indicated by 420. The modulated subcodes θ′_(i) comprising phase-coded waveform 420 extend over a time period divided into substantially equal subpulse widths τ and are phase shifted relative to each other, with the respective phases of each modulated subcode θ′_(i) based on the corresponding random subcode θ_(i). For example at FIG. 4, the modulated subcode θ′_(i) extends over τ₁ with a phase angle at the commencement of τ₁ of p₁, while the modulated subcode θ′₂ extends over τ₂ with a phase angle at the commencement of τ₂ of p₂. Additional phase angles utilized across the time period depicted are generally indicated by circles. As previously discussed, each modulated subcode θ′_(i) is an electromagnetic signal having a frequency and a phase over a subpulse width τ, where the frequency is typically fixed and the phase is dependent on the most recent random subcode θ_(i) received. Modulator 103 communicates the plurality of modulated subcodes θ′_(i) comprising phase-coded waveform 420 to transmitting antenna 104, which transmits phase-coded waveform 420.

Further as previously discussed, polyphase subcode generator 105 produces a polyphase subcode ϕ_(i) corresponding to each random subcode θ_(i). A plurality of polyphase subcodes ϕ_(i) generated by polyphase subcode generator 105 and corresponding to individual random subcodes θ_(i) comprising a plurality of random subcodes θ_(i) is illustrated at FIG. 5. At FIG. 5, the plurality of polyphase subcodes ϕ_(i) extends over a time period with the time period divided into substantially equal subpulse widths τ, and define a phase value between 0 and 360 degrees. Polyphase subcode generator 105 provides a polyphase subcode ϕ_(i) between 0 and 360 at each τ, such as the polyphase subcode ϕ₁ at a first τ, the polyphase subcode ϕ₂ at a second τ, and so on. Each polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having at least N number of members, where N may be any quantity and typically defines some phase-coding scheme. Polyphase subcode generator 105 communicates the polyphase subcodes ϕ_(i) to corrections generator 106, as discussed.

Corrections generator 106 receives each random subcode θ_(i) such as those illustrated at FIG. 3 and a corresponding polyphase subcode ϕ_(i) such as those illustrated at FIG. 5, and generates a phase conversion parameter (ϕ_(i)−θ_(i)) using the subcode θ_(i) and the corresponding polyphase subcode ϕ_(i).

Additionally provided and illustrated at FIG. 6 is an apparatus for a continuous wave radar system 600 comprising one or more digital processors 640, and a monostatic antenna system generally indicated at 641, with monostatic antenna system 641 comprising antenna 604 and circulator 650. The processors 640 are programmed to perform steps comprising generating a random subcode θ_(i) at 601 and generating a polyphase subcode ϕ_(i) corresponding to the random subcode θ_(i) at 605. In particular embodiments, the operations at 601 and 605 are generally synchronized via communication from a clock CLK, as illustrated. As before the polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having N number of members. Processors 640 communicate the subcode θ_(i) and polyphase subcode ϕ_(i) to a corrections generator 606 for generation of a phase conversion parameter (ϕ_(i)−θ_(i)) corresponding to the subcode θ_(i). Processors 640 further communicate the subcode θ_(i) and modulate the subcode θ_(i) producing modulated subcode θ′_(i) at 603, and further communicate the modulated subcode θ′_(i) to antenna system 641, typically via additional amplifying and conditioning components (not shown). Typically CLK is additionally in communication with operation 603 or antenna system 641 in order to enable transmission of the modulated subcode θ′_(i) at a particular transmission time t_(i).

Processors 640 further provide the phase conversion parameter (ϕ_(i)−θ_(i)) to each range gate RG_(j) comprising a plurality of range gates, as previously discussed. Communication of the phase conversion parameter (ϕ_(i)−θ_(i)) occurs following a delay after the transmission time t_(i), with the delay unique to the each range gate RG_(j) as before. This is illustrated at FIG. 6, where processors 640 provide the phase conversion parameter (ϕ_(i)−θ_(i)) to a sequence of operations 642 following the delay D_(j). The sequence of operations 642 is representative of operations previously discussed which occur within a given range gate RG_(j). Having generated the random subcode θ_(i), modulated subcode θ′_(i), and polyphase subcode ϕ_(i) corresponding to a given subpulse width τ, and having generated and provided the phase conversion parameter (ϕ_(i)−θ_(i)) to the sequence of operations 642, at 641, processors 640 repeat the processes and conduct 601, 603, 605, 606, and the appropriate delay D_(j) generally for every subsequent subpulse width τ. This repetition typically occurs independently of any echo processing steps that occur within processors 640. Within the sequence of operations 642 and following the delay D_(j), the phase conversion parameter (ϕ_(i)−θ_(i)) is provided to operation 635, which identifies the most recent phase conversion parameter (ϕ_(k)−θ_(k)). Typically the most recent phase conversion parameter (ϕ_(k)−θ_(k)) is the latest phase conversion parameter (ϕ_(i)−θ_(i)) received. Operation 635 communicates the most recent phase conversion parameter (ϕ_(k)−θ_(k)) to phase conversion operation 612.

As processors 640 conduct operations 601, 603, 605, 606, and D_(j), processors 640 additionally receive modulated echo returns θ′_(R) from antenna system 641, typically via additional amplifying and conditioning components (not shown). Processors 640 demodulates the modulated echo return θ′_(R) at operation 634, generating demodulated subcode θ_(R), as before. Processors 640 provide the demodulated subcode θ_(R) to phase conversion operation 612 which converts the demodulated subcode θ_(R) using the most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from 635, producing an echo subcode ϕ_(R), as before. In some embodiments, CLK is in communication with operation 634 and delay D_(j), in order to indicate when the demodulated subcode θ_(R) is provided by operation 634 and provide an appropriate processing time ΔT_(P(j)) to be utilized in delay D_(j).

Operation 637 adds the resulting echo subcode ϕ_(R) to a polyphase sequence comprising a string of subcodes, illustrated as {ϕ_(R(i)), ϕ_(R(i-i)), ϕ_(R(i-2)), . . . ϕ_(R(N))} at FIG. 6. At operation 638, processors 640 correlate the updated polyphase sequence using the set of polyphase subcodes ϕ_((i)), ϕ_((i-i)), ϕ_((i-2)) . . . ϕ_((N)) utilized in operation 605 using, in certain embodiments, shift register 613 and reference register 615. The correlation provides an output O_(i) which is communicated to integration operation 639. Integration operation 639 subsequently communicates the integrated output to output operation 640.

The method, system, and apparatus provided thereby discloses a manner by which a random CW waveform may be transmitted while enabling the recovery of polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)} advantageous for the purposes of correlation and pulse compression. The apparatus and methodology differs substantially from that employed by typical random radars transmitting randomly phase coded CW waveforms, which generally records and updates a series of echo subcodes received for comparison against a delayed replica for determination of RTT. Further, because the random transmitted waveform is typically correlated against the (also random) delayed replica, any ability to generate advantageous phase codes is lost. In contrast, the system, method, and apparatus disclosed here provides for transmission of a random CW waveform while also allowing the use of any phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} that lends itself to advantageous pulse compressions.

In a typical embodiment, each individual range gate RG_(j) has an associated D_(RG(j)) where the associated D_(RG(j)) is equal to (τ×j)+ΔT_(P(j)), and the phase conversion parameter (ϕ_(i)−θ_(i)) is provided to the each individual range gate RG_(j) such that 0.8≤D_(j)/D_(RG(j))≤1.2, where D_(j) is the delay D_(j) unique to the each individual range gate RG_(j) and D_(RG(j)) is the associated D_(RG(j)). In certain embodiments, 0.9≤D_(j)/D_(RG(j))≤1.1, and in other embodiments, 0.95≤D_(j)/D_(RG(j))≤1.05. The associated processing time period ΔT_(P(j)) may differ among the various range gates RG_(j), or may be a time period common to all range gates.

In other embodiments, the digital process, analog process, or combination used to generate the specific phase conversion parameter (ϕ_(i(S))−θ_(i(S))) performs operations equivalent to (ϕ_(i(S))−θ_(i(S)))=f₁(ϕ_(i(S)), θ_(i(S))) where f₁ is a mathematical function over at least some portion of a domain comprising ϕ_(i(S)) and θ_(i(S)), and where (ϕ_(i(S))−θ_(i(S))) is the specific phase conversion parameter (ϕ_(i(S))−θ_(i(S))), ϕ_(i(S)) is the specific polyphase subcode ϕ_(i(S)), and θ_(i(S)) is the specific random subcode θ_(i(S)).

In another embodiment, phase conversion module 212 performs operations equivalent to ϕ_(R(S))=f₂((ϕ_(k)−θ_(k))_((S)), θ_(R(S))) where f₂ is a mathematical function over at least some portion of a domain comprising (ϕ_(k)−θ_(k))_((S)) and θ_(R(S)), and where when 0.8≤θ_(i(S))/θ_(R(S))≤1.2 and 0.8≤(ϕ_(i(S))−θ_(i(S)))/(ϕ_(k)−θ_(k))_((S))≤1.2, then 0.8≤ϕ_(i(S))/ϕ_(R(S))≤1.2, where θ_(i(S)) is one of the random subcodes θ_(i) generated by the random wave form generator, ϕ_(i(S)) is the specific polyphase subcode ϕ_(i(S)) generated by the corrections generator for the θ_(i(S)), θ_(R(S)) is the specific demodulated subcode θ_(R(S)), (ϕ_(i(S))−θ_(i(S))) is the specific phase conversion parameter (ϕ_(i(S))−θ_(i(S))) generated by the corrections generator for the θ_(i(S)) and ϕ_(i(S)), and (ϕ_(k)−θ_(k))_((S)) is the specific most recent phase conversion parameter (ϕ_(k)−θ_(k))_((S)). In other embodiments, the function f₂ is substantially an inverse function of the function f₁ used by corrections generator 106, such that when (ϕ_(i(S))−θ_(i(S))=f₁(ϕ_(i(S)), θ_(i(S))) and a ϕ₀=f₂((ϕ_(i(s))−θ_(i(S)))_((S)), θ_(i(S))), then 0.8≤ϕ_(i(S))/ϕ₀≤1.2. In certain embodiments when 0.9≤θ_(i(S))/θR(S)≤1.1 and 0.9≤(ϕ_(i(S))−θ_(i(S))/(ϕ_(k)−θ_(k))_((S))≤1.1 then 0.9≤ϕ_(i(S))/ϕ_(R(S))≤1.1, and in other embodiments when 0.95≤θ_(i(S))/θ_(R(S))≤1.05 and 0.95≤(ϕ_(i(S))−θ_(i(S)))/(ϕ_(k)−θ_(k))_((S))≤1.05 then 0.95≤ϕ_(i(S))/ϕ_(R(S))≤1.05. In some embodiments when (ϕ_(i(S))−θ_(i(S)))=f₁(ϕ_(i(S)), θ_(i(S))) and the ϕ₀=f₂((ϕ_(i(s))−θ_(i(S))), θ_(i(S))), then 0.9≤ϕ_(i(S))/ϕ₀≤1.1, and in further embodiments then 0.95≤ϕ_(i(S))/ϕ₀≤1.05.

Additionally, in some embodiments, a “random subcode θ_(i)” means one of a plurality of random subcodes θ_(i), where the plurality of random subcodes θ_(i) defines a plurality of phases over some time period and the plurality of phases over the time period generally comprises a probability density function (μ,σ²) having a mean μ and a variance σ², such as a Normal, Beta, Uniform, Weibull, or other distributions known in the art. In some embodiments, each phase p comprising the plurality of phases satisfies a relationship 0.8≤p/x_(PDF)≤1.2, where x_(PDF) is a point on the probability density function (μ,σ²). In other embodiments 0.9≤p/x_(PDF)≤1.1, and in other embodiments 0.95≤p/x_(PDF)≤1.05. The generation of such random phases may be conducted using means known in the art, such as noise-generating microwave sources, digital generation using a processor, or others. See e.g., Axellson, “Noise Radar Using Random Phase and Frequency Modulation,” IEEE Transactions on Geoscience and Remote Sensing 42(11) (2004), and see K. Kulpa, Signal Processing in Noise Waveform Radar (2013), and see G. R. Cooper and C. D. McGillem, Random Signal Radar, Final Rep. TR-EE67-11 (1967), among many others.

Further and in other embodiments, “modulated subcode θ′_(i)” means an electromagnetic signal having a frequency and a phase over a subpulse width τ, where the phase defines a value of the modulated subcode θ′_(i) at some point during the subpulse width τ, and where the phase is based on a random subcode θ_(i). In certain embodiments, the phase defines the value of the modulated subcode θ′_(i) at the commencement of the subpulse width τ. In certain embodiments, the phase is a mathematical function of the random subcode θ_(i). In other embodiments, a parameter P₀ is a function of a specific random subcode θ_(i(P)) such that P₀=f₃(θ_(i(P))) where θ_(i(P)) denotes the specific random subcode θ_(i(P)) and where f₃ is a mathematical function over at least some portion of a domain comprising θ_(i(P)), and the phase for the specific random subcode θ_(i(P)) has a value such that 0.8≤p/P₀≤1.2 in one embodiment, 0.9≤p/P₀≤1.1 in a another embodiment, and 0.95≤p/P₀≤1.05 in a further embodiment, where p is the phase of the modulated subcode θ′_(i). In other embodiments, the frequency of the modulated subcode θ′_(i) is constant over the subpulse width τ.

Additionally, it is understood that although the foregoing discussions discuss generation of an individual random subcode θ_(i), in preparation for transmitting a specific modulated subcode θ′_(i) at a transmission time t_(i), and generation of an individual polyphase subcode ϕ_(i) corresponding to the specific modulated subcode θ′_(i), and generation of an individual phase correction parameter (ϕ_(i)−θ_(i)) corresponding to the specific modulated subcode θ′_(i), it is not required that generation of the individual random subcode θ_(i), the individual polyphase subcode ϕ_(i), or the individual phase correction parameter (ϕ_(i)−θ_(i)) be temporally related to the transmission time t_(i) of the specific modulated subcode θ′_(i) except to the extent necessary for a modulator such as 103 to upconvert a random subcode θ_(i) to a modulated subcode θ′_(i) and for a corrections generator such as 106 to provide a properly delayed phase correction parameter (ϕ_(i)−θ_(i)) comprising the random subcode θ_(i) corresponding to the modulated subcode θ′_(i).

Further, it is understood that CW system 100 is typically intended to operate as a continuous wave radar system exhibiting a high duty cycle, where here “duty cycle” means the proportion of a given time period when transmitting antenna 104 emits modulated subcodes θ′_(i). In certain embodiments. CW System 100 exhibits a duty cycle of at least ½, in other embodiments at least 7/10, and in further embodiments at least 9/10.

Further it is understood that, although FIG. 1 depicts a bistatic system comprising both transmitting antenna 104 and a separate receiving antenna 108, this is not intended as a limitation on the disclosure. Alternatively, CW system 100 could be a monostatic system where transmitting antenna 104 and receiving antenna 108 are a single antenna, and communications from modulator 103 and to demodulator 109 are directed using a circulator, as is known in the art of CW radar systems.

Further it is understood that the functions of various components described herein may be performed using analog or digital means. In certain embodiments, CW system 100 comprises one or more digital processors, and the one or more digital processors are programmed with instructions for performing some or all of the functions of random waveform generator 101, modulator 103, polyphase subcode generator 105, corrections generator 106, the plurality of range gates RG_(j), or various combinations thereof.

FIGS. 7 and 8 illustrate a specific embodiment of the manner in which the random waveform generator 101, polyphase subcode generator 105, and corrections generator 106 of CW system 100 act to provide a properly delayed most recent phase conversion parameter (ϕ_(k)−θ_(k)) to each range gate in order to allow recovery of underlying polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)}. FIG. 7 illustrates a series of parameters generally indicated by random subcode θ_(i), polyphase subcode ϕ_(i), phase conversion parameter (ϕ_(i)−θ_(i)), and modulated subcode θ′_(i) generated by CW system 100 in support of transmitting the modulated subcodes via transmitting antenna 104 over time periods generally indicated by Transmission time L. In support of transmission at the Transmission time t_(i) of 0<t₁≤1τ, random waveform generator 101 generates the random subcode θ₁, and polyphase subcode generator 105 produces the polyphase subcode ϕ₁ corresponding to the random subcode θ₁. Random waveform generator 101 communicates the random subcode θ₁ and polyphase subcode generator 105 communicates the polyphase subcode ϕ₁ to corrections generator 106, which generates the phase conversion parameter (ϕ₁−θ₁) corresponding to the random subcode θ₁. Additionally, random waveform generator 101 communicates random subcode θ₁ to modulator 103 which upconverts random subcode θ₁ to modulated subcode θ′₁, and transmitting antenna 104 transmits the modulated subcode θ′₁ over the transmission time 0<t₁≤1τ. Similarly in support of transmission at the Transmission time t_(i) of 1τ<t₁≤2τ, random waveform generator 101 generates random subcode θ₂, polyphase subcode generator 105 produces polyphase subcode ϕ₂, corrections generator 106 generates phase conversion parameter (ϕ₂−θ₂), and further random waveform generator 101 communicates random subcode θ₂ to modulator 103 for upconversion and transmission of modulated subcode θ′₂ via transmitting antenna 104 over Transmission time 1τ<t₂≤2τ. Similar operations occur for transmission of modulated subcode θ′₃ over 2τ<t₃≤3τ, modulated subcode θ′₄ over 3τ<t₄≤4τ, modulated subcode θ′₅ over 4τ<t_(s)≤5τ, modulated subcode θ′₆ over 5τ<t₆≤6τ, modulated subcode θ′₇ over 6τ<t₇≤7τ, modulated subcode θ′₈ over 7τ<t₈≤8τ, and modulated subcode θ′₉ over 8τ<t₉≤9τ. As previously discussed, all random subcode θ_(i) are random phases, and all modulated subcodes θ′_(i) transmitted are randomly phase coded waveforms. Note also that in this illustration, polyphase subcode generator 105 utilizes a set of repeating polyphase subcodes {ϕ₁, ϕ₂, ϕ₃}, such that corrections generator 106 generates sequential phase conversion parameters of (ϕ₁−θ₁), (ϕ₂−θ₂), (ϕ₃−θ₃), (ϕ₁−θ₄), (ϕ₂−θ₅), (ϕ₃−θ₆), (ϕ₁−θ₇), (ϕ₂−θ₈), and (ϕ₃−θ₉).

FIG. 8 illustrates the transmission of the modulated subcodes θ′_(i) from transmitting antenna 104 over the transmission periods generally indicated by t_(i). For illustration, the transmission commences with transmitting antenna 104 transmitting the modulated subcode θ′₁ over 0<t₁≤1τ, and the presence of θ′₁ as a waveform physically present within a range interval is similarly illustrated at FIG. 8 using range intervals generally indicated by RH₀, RH₁, RH₂, and RH₃, whereas before the range intervals correspond to a distance substantially equivalent to τc/2. Accordingly, transmitting antenna 104 transmits modulated subcode θ′₂ over 1τ<t₂≤2τ, modulated subcode θ′₃ over 2τ<t₃≤3τ, and so on to the last illustrated transmission where transmitting antenna 104 transmits modulated subcode θ′₉ over 8τ<t₂≤9τ.

FIG. 8 additionally illustrates a plurality of range gates RG₁, RG₂, and RG₃. The transmission times ti of FIG. 8 apply to all parameters horizontally level with a given ti, and the phase conversion parameters sent to the plurality of range gates RG₁, RG₂, and RG₃ from corrections generator 106 following appropriate delay are additionally indicated at each time and for each of RG₁, RG₂, and RG₃. The particular phase conversion parameters indicated for each range gate and at each time are the most recent phase conversion parameters (ϕ_(k)−θ_(k)) discussed earlier and received by phase conversion module 212, based on the appropriate range delay for a given range gate. For example, for the ti commencing at zero and treating a ΔT_(P(1)) as equal to zero for the purpose of illustration, RG₁ receives the phase correction (ϕ₁−θ₁) during the period 1τ<t₃≤2τ, based on the delay τ(1)+0=1τ. Similarly, for the t_(i) commencing at 1τ, RG₁ receives phase correction (ϕ₂−θ₂) during the period 2τ<t₃≤3τ based on the appropriate delay 1τ, and, for the t_(i) commencing at 2τ, receives (ϕ₃−θ₃) during the period 3τ<t₄≤4τ based on the appropriate delay 1τ. RG₁ continues to receive most recent phase corrections having the appropriate 1τ delay for each corresponding modulated subcode θ′_(i) transmitted, through to reception of (ϕ₂−θ₈) during period 8τ<t₉≤9τ.

In similar fashion, for the t_(i) commencing at zero and with a ΔT_(P(2)) equal to zero, RG₂ receives the phase correction (ϕ₁−θ₁) during the period 2τ<t₃≤3τ, based on the delay τ(2)+0=2τ. For the t_(i) commencing at 1τ, RG₂ receives phase correction (ϕ₂−θ₂) during the period 3τ<t₄≤4τ based on the appropriate delay 2τ, and for the t_(i) commencing at 2τ, receives (ϕ₃−θ₃) during the period 4τ<t₅≤5τ based on the appropriate delay 2τ, and so on through to reception of (ϕ₁−θ₇) during period 8τ<t₉≤9τ. In like manner, for the t commencing at zero and with ΔT_(P(3)) equal to zero, RG₃ receives the phase correction (ϕ₁−θ₁) during the period 3τ<t₄≤4τ, based on the delay τ(3)+0=3τ, and for the t_(i) commencing at 1τ receives phase correction (ϕ₂−θ₂) during the period 4τ<t₅≤5τ based on the appropriate delay 3τ, and for the t_(i) commencing at 2τ, receives (ϕ₃−θ₃) during the period 5τ<t₆≤6τ based on the appropriate delay 3τ. As previously discussed, each respective range gate RG₁, RG₂, and RG₃ utilizes its most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from corrections generator 106 to phase rotate any demodulated subcode θ_(R) received from demodulator 109, in order to generate an echo subcode ϕ_(R) from the demodulated subcode θ_(R).

The impact of the phase conversions based on the properly delayed phase correction parameters (ϕ_(i)−θ_(i)) is illustrated at FIG. 9, which similar to FIG. 8 illustrates the transmission of modulated subcodes θ′_(i) from transmitting antenna 104, range intervals RH₀, RH₁, RH₂, and RH₃, range gates RG₁, RG₂, and RG₃, and also the properly delayed most recent phase conversion parameters (ϕ_(k)−θ_(k)) for each range gate corresponding to the listed transmission times. FIG. 9 additionally illustrates demodulated subcodes θ_(R) provided by demodulator 109 and arising from an object O₁ located in range interval RH₁. Based on the range intervals of τc/2 and the inherent round trip time (RTT) from the object O₁ in RH₁, and for a transmission of a modulated subcode θ′₁ commencing at t_(i) of zero, and again for illustration using a processing time ΔT_(P) equal to zero, each range gate RG₁, RG₂, and RG₃ is expected to initially receive the demodulated subcode θ₁ of the echo from demodulator 109 during the time interval over 1τ<t₂≤2τ, as illustrated for each range gate. In similar fashion and based on the expected RTT corresponding to the object O₁, RG₁, RG₂, and RG₃ each receive the demodulated subcode θ₂ of the echo during 2τ<t₃≤3τ. Additionally at 2τ<t₃≤3τ and due to the range interval of τc/2, RG₁, RG₂, and RG₃ also receives the back half of the demodulated subcode θ₁, as indicated. Similarly and for similar reasons, RG₁, RG₂, and RG₃ receive demodulated subcode θ₃ and θ₂ of the echo during 3τ<t₅≤4τ, the demodulated subcode θ₄ and θ₃ of the echo during 4τ<t₅≤5τ, and so on to the reception of the demodulated subcode θ₈ and θ₇ of the echo during 8τ<t₉≤9τ. Similar to FIG. 8, for each range gate, the most recent phase conversion parameters (ϕ_(k)−θ_(k)) provided to the phase conversion module 212 of each respective range gate is additionally indicated. For illustrative purposes at FIG. 9, leakage signals contributions are ignored but will be discussed subsequently.

As can be recognized at FIG. 9, beginning at 1τ<t₂≤2τ, for an object O₁ located within RH₁, the most recent most recent phase conversion parameter (ϕ_(k)−θ_(k)) provided to RG₁ in conjunction with the demodulated subcode θ_(R) present at the range gates allows the phase conversion module of RG₁ to phase rotate the demodulated subcode θ_(R) and produce an echo subcode ϕ_(R−1) generally equivalent to one of the repeating ϕ₁, ϕ₂, or ϕ₃ polyphase subcodes utilized by polyphase subcode generator 105 in this example. For example, phase conversions by a phase conversion module such as 212 would substantially produce echo subcodes ϕ_(R-1) of ϕ₁ at 1τ<t₃≤2τ, ϕ₂ at 2τ<t₃≤3τ, ϕ₃ at 3τ<t₄≤4τ, again at 4τ<t₅≤5τ, ϕ₂ at 5τ<t₆≤6τ, ϕ₃ at 6τ<t₇≤7τ, and again ϕ₁ at 7τ<t₈≤8τ, and ϕ₂ at 8τ<t₉≤9τ. Relative to a shift register such as 213 and a reference register 215 comprising the ϕ₁, ϕ₂, and ϕ₃ polyphase subcodes, matched filter 214 would generate optimized pulse compressions generally each time the phase conversion module 212 adds the resulting echo subcode ϕ_(R-1) to the string of subcodes and {ϕ₁, ϕ₂, ϕ₃} are ordered within shift register 213. Meanwhile at FIG. 9, because of the delayed phase conversion parameters (ϕ_(k)−θ_(k)) present at RG₂ and RG₃, phase conversions do not produce one of ϕ₁, ϕ₂, or ϕ₃ but rather generate another random subcode φ_(random), and the respective matched filters of those range gates substantially generate noise signals. Thus for the object O₁ within the range interval RH₁, the properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) provided to each range gate generates pulse compression in the appropriate range bin while generally resulting in noise generation in other range bins.

FIG. 10 illustrates the impact of the properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) based on demodulated subcodes θ_(R) provided by demodulator 109 and arising from an object O₂ located in range interval RH₂. As illustrated, beginning at 2τ<t₃≤3τ, for the object O₂ within RH₂, the most recent most recent phase conversion parameter (ϕ_(k)−θ_(k)) provided to RG₂ allows the phase conversion module of RG₂ to phase rotate the demodulated subcode θ_(R) and produce echo subcodes ϕ_(R-2) generally equivalent to one of ϕ₁, ϕ₂, or ϕ₃. The properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) provided to the remaining range gates produce additional random subcodes φ_(random).

FIG. 11 illustrates the impact of the properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) when CW system receives demodulated subcodes θ_(R) provided by demodulator 109 and arising concurrently from an object O₁ in range interval RH₁, an object O₂ in range interval RH₂, and an object O₃ in range interval RH₃. As before, based on range intervals of τc/2 and the expected RTT for O₁ in RH₁, each range gate would initially receive the demodulated subcode θ₁ during the time interval over 1τ<t₂≤2τ, and chronologically receive θ₂ through θ₈ over the remaining time intervals illustrated, as well as the back half during subsequent time periods as before. Similarly and in addition, and based on the expected RTT for O₂ in RH₂, each range gate would further begin receiving the demodulated subcode θ₁ during the time interval over 2τ<t₃≤3τ, and due to continuing echoes from O₂ chronologically receive θ₁ through θ₇ over the remaining time intervals illustrated. Further, and based on the expected RTT for O₃ in RH₃, each range gate would additionally begin receiving the demodulated subcode θ₁ during the time interval over 3τ<t₄≤4τ, and due to continuing echoes from O₃ chronologically receive θ₂ through θ₆ over the remaining time intervals illustrated. As a result, each range gates receives multiple demodulated echoes. However, due to the properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) also illustrated at FIG. 11 for each range gate, the subsequent phase conversions of RG₁ will largely produce echo subcodes ϕ_(R-1) approximating ϕ₁ at 1τ<t₂≤2τ, ϕ₂ at 2τ<t₃≤3τ, ϕ₃ at 3τ<t₄≤4τ, ϕ₁ at 4τ<t₅≤5τ, ϕ₂ at 5τ<t₆≤6τ, ϕ₃ at 6<t₇≤7τ, ϕ₁ at 7τ<t₈≤8τ, and ϕ₂ at 8τ<t₉≤9τ, while the phase conversions of RG₂ will largely produce echo subcodes ϕ_(R-2) approximating ϕ₁ at 2τ<t₃≤3τ, ϕ₂ at 3τ<t₄≤4τ, ϕ₃ at 4τ<t₅≤5τ, ϕ₁ at 5τ<t₆≤6τ, ϕ₂ at 6τ<t₇≤7τ, ϕ₃ at 7τ<t₈≤8τ, and ϕ₄ at 8τ<t₉≤9τ, while the phase conversions of RG₃ will largely produce echo subcodes ϕ_(R-3) approximating ϕ₁ at 3τ<t₄≤4τ, ϕ₂ at 4τ<t₅≤5τ, ϕ₃ at 5τ<t₆≤6τ, ϕ₁ at 6τ<t₇≤7τ, ϕ₂ at 7τ<t₈≤8τ, and ϕ₃ at 8τ<t₉≤9τ. Thus, as disclosed, CW system 100 provides the significant capability of enabling the recovery of an underlying phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} following return of a modulated echo θ′_(R), using a randomly phase coded CW waveform.

In addition to the advantage of enabling recovery of the underlying phase code {ϕ₁, ϕ₂, . . . ϕ_(N)}, the use of the delayed phase code corrections in the manners described additionally has the significant advantage of allowing for CW transmission while minimizing the impact of signal leakage. As is understood and as discussed above, in any CW system, during an analogous transmission of a modulated subcode θ′_(i) at a time t_(i), some degree of leakage of the modulated subcode θ′_(i) is experienced by the receiving components of the system, degrading the ability of the receiving components to separate and discriminate a modulated echo θ′_(R). However, the particular manner of providing phase conversion parameters to the respective range gates provided by this disclosure act to significantly mitigate the impact of this leakage in any subsequent processing. This is illustrated at FIG. 12 which, similar to FIG. 10, illustrates demodulated subcodes θ_(R) provided to RG₁, RG₂, and RG₃ arising from an object O₂ located in range interval RH₂. In addition, in parenthesis and italicized, leakage signals received by each range gate are also indicated based on the current modulated subcode θ′_(i) being transmitted via transmitting antenna 104. FIG. 12 also illustrates the properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) provided to each range gate RG_(j), including those phase conversion parameters that correspond to prior modulated subcodes θ′_(i) (not shown) that preceded the transmission of θ′₁ during 0<t₁≤1τ. The prior phase conversion parameters which precede (ϕ₁−θ₁) are indicated as (ϕ₀−θ₀), (ϕ⁽⁻¹⁾−θ⁽⁻¹⁾), and (ϕ⁽⁻²⁾−θ⁽⁻²⁾). At FIG. 12, and as a result of the properly delayed phase conversion parameters provided to each range gate, conversion of the leakage signals using the most recent phase conversion parameter (ϕ_(k)−θ_(k)) at each respective range gate acts to generate another random subcode φ_(random), rather than one of ϕ₁, ϕ₂, or ϕ₃. However, beginning at 2τ<t₃≤3τ as before, for the object O₂ within RH₂, the most recent most recent phase conversion parameter (ϕ_(k)−θ_(k)) provided to RG₂ allows the phase conversion module of RG₂ to phase rotate the demodulated subcode θ_(R) and produce echo subcodes ϕ_(R−2) generally equivalent to one of ϕ₁, ϕ₂, or ϕ₃. The properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) thereby significantly mitigate the impact of any leakage signals on CW system 100 that arise from the modulated subcode θ′_(i) currently being transmitted.

Thus, provided here is method, system, and apparatus by which a random CW radar waveform may be transmitted while enabling the recovery of polyphase subcodes {ϕ₁, ϕ₂, ϕ₃, . . . ϕ_(N)} advantageous for the purposes of correlation and pulse compression. The CW system transmits and receives a random waveform while avoiding the necessary use of a delayed replica for RTT determination, by providing properly delayed phase conversion parameters (ϕ_(i)−θ_(i)) from a corrections generator to various range gates RG_(j) comprising a plurality of range gates. The associated methodology of the CW radar system has the significant advantage of enabling recovery of the underlying phase code {ϕ₁, ϕ₂, . . . θ_(N)} associated with a given {θ₁, θ₂, . . . θ_(N)} series of modulated subcodes θ′_(i) transmitted, based on the phase conversion parameters (ϕ_(i)−θ_(i)) appropriately delayed and provided by the corrections generator. This allows use of any phase code {ϕ₁, ϕ₂, . . . ϕ_(N)} that lends itself to advantageous pulse compressions while concurrently enabling transmission of a randomly phase-coded waveform.

Accordingly, this description provides exemplary embodiments of the present invention. The scope of the present invention is not limited by these exemplary embodiments. Numerous variations, whether explicitly provided for by the specification or implied by the specification or not, may be implemented by one of skill in the art in view of this disclosure.

It is to be understood that the above-described arrangements are only illustrative of the application of the principles of the present invention and it is not intended to be exhaustive or limit the invention to the precise form disclosed. Numerous modifications and alternative arrangements may be devised by those skilled in the art in light of the above teachings without departing from the spirit and scope of the present invention. It is intended that the scope of the invention be defined by the claims appended hereto.

In addition, the previously described versions of the present invention have many advantages, including but not limited to those described above. However, the invention does not require that all advantages and aspects be incorporated into every embodiment of the present invention.

All publications and patent documents cited in this application are incorporated by reference in their entirety for all purposes to the same extent as if each individual publication or patent document were so individually denoted. 

What is claimed is:
 1. A method of transmitting a continuous wave phase-modulated random radar signal and processing echo returns comprising: generating the continuous wave phase-modulated random radar signal by: generating a random subcode θ_(i); producing a polyphase subcode ϕ_(i) corresponding to the random subcode θ_(i) where the polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having N number of members; transmitting a modulated subcode θ′_(i) from an antenna system during a subpulse width τ where τ is a measure of time, and where the modulated subcode θ′_(i) is an electromagnetic signal having a phase over the subpulse width τ, where the phase is based on the random subcode θ_(i); generating a phase conversion parameter (ϕ_(i)−θ_(i)) using the random subcode θ_(i) and the polyphase subcode ϕ_(i) and providing the phase conversion parameter (ϕ_(i)−θ_(i)) to a plurality of range gates comprising two or more range gates RG_(j), where j is an integer unique to each range gate RG_(j) and j is greater than or equal to 1, by providing the phase conversion parameter (ϕ_(i)−θ_(i)) to the each individual range gate RG_(j) following a delay D_(j) after transmission of the modulated subcode θ′_(i) from the antenna system, where the delay D_(j) is unique to the each individual range gate RG_(j); and repeating the generating the random subcode θ_(i) step, the producing the polyphase subcode ϕ_(i) step, the transmitting the modulated subcode θ′_(i) step, and the generating the phase conversion parameter (ϕ_(i)−θ_(i)) using the random subcode θ_(i) and the polyphase subcode ϕ_(i) and providing the phase conversion parameter (ϕ_(i)−θ_(i)) step, thereby transmitting the continuous wave phase-modulated random radar signal; and receiving an echo return of the continuous wave phase-modulated random radar signal and processing the echo return using the plurality of range gates RG_(j), thereby processing echo returns.
 2. The method of claim 1 where receiving the echo return of the continuous wave phase-modulated random radar signal and processing the echo return using the plurality of range gates RG_(j) further comprises: receiving the echo return from the antenna system; demodulating the echo return and producing a demodulated subcode θ_(R); and providing the demodulated subcode θ_(R) to the plurality of range gates RG_(j).
 3. The method of claim 2 further comprising processing the demodulated subcode θ_(R) by, at the each range gate RG_(j) by performing steps comprising: receiving the demodulated subcode θ_(R); identifying a most recent phase conversion parameter (ϕ_(k)−θ_(k)) received from the corrections generator, where the most recent phase conversion parameter (ϕ_(k)−θ_(k)) is the phase conversion parameter (ϕ_(i)−θ_(i)) most recently provided to the each range gate RG_(j); generating an echo subcode ϕ_(R) by converting the demodulated subcode θ_(R) using the most recent phase conversion parameter (ϕ_(k)−θ_(k)); modifying a polyphase sequence comprising a string of subcodes by adding the echo subcode ϕ_(R) to the polyphase sequence, thereby generating an updated polyphase sequence; and correlating the updated polyphase sequence using the set of polyphase subcodes having N number of members used by the polyphase subcode generator, thereby processing the demodulated subcode θ_(R).
 4. The method of claim 3 where the each range gate RG_(j) has an associated D_(RG(j)) where the associated D_(RG(j)) is equal to 2τ(j)+ΔT_(P), where ΔT_(P) is a period ΔT_(P) based on an echo processing delay, and where 0.8≤D_(j)/D_(RG(j))≤1.2, where D_(j) is the delay D_(j) unique to the each range gate RG_(j) and D_(RG(j)) is the associated D_(RG(j)) for the each range gate RG_(j).
 5. The method of claim 4 further comprising providing the demodulated subcode θ_(R) to the plurality of range gates RG_(j) over the period ΔT_(P).
 6. The method of claim 5 where correlating the updated polyphase sequence using the set of polyphase subcodes having N number of members comprises correlating the updated polyphase sequence using a matched filter comprising a reference register, where the reference register comprises the set of polyphase subcodes having N number of members used by the polyphase subcode generator, thereby processing the demodulated subcode θ_(R).
 7. The method of claim 5 where generating the phase conversion parameter (ϕ_(i)−θ_(i)) using the random subcode θ_(i) and the polyphase subcode ϕ_(i) comprises performing operations equivalent to (ϕ_(i)−θ_(i))=f₁(ϕ_(i), θ_(i)) where f₁ is a mathematical function over at least some portion of a domain comprising ϕ_(i) and θ_(i), and where (ϕ_(i)−θ_(i)) is the phase conversion parameter (ϕ_(i)−θ_(i)), ϕ_(i) is the polyphase subcode ϕ_(i), and θ_(i) is the random subcode θ_(i).
 8. The method of claim 7 where generating the echo subcode ϕ_(R) by converting the demodulated subcode θ_(R) using the most recent phase conversion parameter (ϕ_(k)−θ_(k)) comprises performing operations equivalent to ϕ_(R)=f₂((ϕ_(k)−θ_(k)), θ_(R)), where f₂ is a mathematical function over at least some portion of a domain comprising (ϕ_(k)−θ_(k)) and θ_(R) and where when 0.8≤θ_(i)/θ_(R)≤1.2 and 0.8≤(ϕ_(i)−θ_(i))/(ϕ_(k)−θ_(k))≤1.2, then 0.8≤ϕ_(i)/ϕ_(R)≤1.2, where θ_(R) is the demodulated subcode θ_(R), (ϕ_(k)−θ_(k)) is the most recent phase conversion parameter (ϕ_(k)−θ_(k)), and ϕ_(R) is the echo subcode θ_(R).
 9. The method of claim 5 where the continuous wave phase-modulated random radar signal comprises a plurality of random subcodes θ_(i) where the plurality of random subcodes θ_(i) defines a plurality of phases over a time period T, and each phase comprising the plurality of phases satisfies a relationship 0.8≤p/x_(PDF)≤1.2, where p is the each phase comprising the plurality of phases and x_(PDF) is a point on a probability density function (μ,τ²).
 10. A system for transmitting a randomly modulated subcode and processing echo returns: a transmitting system comprising: a random waveform generator receiving a random noise signal and generating a random subcode θ_(i), where the random subcode θ_(i) has a subpulse width τ where τ is a measure of time; a polyphase subcode generator producing a polyphase subcode ϕ_(i) corresponding to the random subcode θ_(i) where the polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having N number of members; an antenna system transmitting a modulated subcode θ′_(i) at a time t_(i), where the modulated subcode θ′_(i) is an electromagnetic signal having a frequency and having a phase over the subpulse width τ dependent on the random subcode θ_(i), thereby transmitting the randomly modulated subcode; and a corrections generator performing steps comprising: receiving the random subcode θ_(i) from the random waveform generator; receiving the polyphase subcode ϕ_(i) from the polyphase subcode generator; and generating a phase conversion parameter (ϕ_(i)−θ_(i)) using the random subcode θ_(i) and the polyphase subcode ϕ_(i) and providing the phase conversion parameter (ϕ_(i)−θ_(i)) to a plurality of range gates comprising two or more range gates RG_(j), where j is an integer unique to each range gate RG_(j) and j is greater than or equal to 1, by providing the phase conversion parameter (ϕ_(i)−θ_(i)) to the each range gate RG_(j) following a delay D_(j) after transmission of the modulated subcode θ′_(i) from the antenna system, where the delay D_(j) is unique to the each range gate RG_(j); the antenna system receiving an echo return of the modulated subcode θ′_(i) transmitted by the antenna system; a demodulator receiving the echo return and demodulating the echo return to produce a demodulated subcode θ_(R), and providing the demodulated subcode θ_(R) to the plurality of range gates; the each range gate RG_(j) receiving the demodulated subcode θ_(R) and receiving the phase conversion parameter (ϕ_(i)−θ_(i)) following the delay D_(j), and the each range gate RG_(j) processing the demodulated subcode θ_(R), thereby processing echo returns.
 11. The system of claim 10 further comprising the demodulator receiving the echo return and demodulating the echo return to produce a demodulated subcode θ_(R) and providing the demodulated subcode θ_(R) to the plurality of range gates over a period ΔT_(P).
 12. The system of claim 11 further comprising the corrections generator providing the phase conversion parameter (ϕ_(i)−θ_(i)) to the each range gate RG_(j) using an associated D_(RG(j)) for the each range gate RG_(j), where the associated D_(RG(j)) for the each range gate RG_(j) is equal to 2τ(j)+ΔT_(P), and where 0.8≤D_(j)/D_(RG(j))≤1.2, where D_(j) is the delay D_(j) unique to the each range gate RG_(j) and D_(RG(j)) is the associated D_(RG(j)) for the each range gate RG_(j).
 13. The system of claim 12 further comprising the each range gate RG_(j) processing the demodulated subcode θ_(R) by: generating an echo subcode ϕ_(R) by converting the demodulated subcode θ_(R) using the phase conversion parameter (ϕ_(i)−θ_(i)) received from the corrections generator following the delay D_(j); modifying a polyphase sequence comprising a string of subcodes by adding the echo subcode ϕ_(R) to the polyphase sequence, thereby generating an updated polyphase sequence; and correlating the updated polyphase sequence using the set of polyphase subcodes having N number of members used by the polyphase subcode generator, thereby processing the demodulated subcode θ_(R).
 14. The system of claim 13 further comprising: the corrections generator generating the phase conversion parameter (ϕ_(i)−θ_(i)) by performing operations equivalent to (ϕ_(i)−θ_(i))=f₁(ϕ_(i), θ_(i)) where f₁ is a mathematical function over at least some portion of a domain comprising ϕ_(i) and θ_(i), and where (ϕ_(i)−θ_(i)) is the phase conversion parameter (ϕ_(i)−θ_(i)), ο_(i) is the polyphase subcode ϕ_(i), and θ_(i) is the random subcode θ_(i); the each range gate RG_(j) generating the echo subcode ϕ_(R) by performing operations equivalent to ϕ_(R)=f₂((ϕ_(k)−θ_(k)), θ_(R)), where f₂ is a mathematical function over at least some portion of a domain comprising (ϕ_(k)−θ_(k)) and θ_(R) and where when 0.8≤θ_(i)/θ_(R)≤1.2 and 0.8≤(ϕ_(i)−θ_(i))/(ϕ_(k)−θ_(k))≤1.2, then 0.8≤ϕ_(i)/ϕ_(R)≤1.2, where θ_(R) is the demodulated subcode θ_(R), (ϕ_(k)−θ_(k)) is the most recent phase conversion parameter (ϕ_(k)−θ_(k)), and ϕ_(R) is the echo subcode ϕ_(R).
 15. The system of claim 14 further comprising: the random waveform generator using a plurality of random noise signals and generating a plurality of random subcodes θ_(i), where the plurality of random subcodes θ_(i) defines a plurality of phases over a time period T, and where each phase comprising the plurality of phases satisfies a relationship 0.8≤p/x_(PDF)≤1.2, where p is the each phase comprising the plurality of phases and x_(PDF) is a point on a probability density function (μ,σ²), and; the antenna system transmitting a plurality of modulated subcodes θ′_(i) where every modulated subcode θ′_(i) in the plurality of modulated subcodes θ′_(i) is an electromagnetic signal having a frequency and having a phase over the subpulse width τ dependent on one of the random subcodes θ_(i), comprising the plurality of random subcodes θ_(i).
 16. A Continuous Wave Radar Apparatus comprising: one or more digital processors programmed to generate a plurality of random subcodes, communicate a plurality of phase conversion parameters, and process echo returns by performing steps comprising: I) generating a random subcode θ_(i); II) producing a polyphase subcode ϕ_(i) corresponding to the random subcode θ_(i) where the polyphase subcode ϕ_(i) is a member of a set of polyphase subcodes having N number of members; III) generating a phase conversion parameter (ϕ_(i)−θ_(i)) using the random subcode θ_(i) and the polyphase subcode ϕ_(i) and providing the phase conversion parameter (ϕ_(i)−θ_(i)) to a plurality of range gates comprising two or more range gates RG_(j), where j is an integer unique to each range gate RG_(j) and j is greater than or equal to 1, by providing the phase conversion parameter (ϕ_(i)−θ_(i)) to the each range gate RG_(j) following a delay D_(j) after a transmission time t_(i), where the delay D_(j) is unique to the each range gate RG_(j); IV) generating a modulated subcode θ′_(i) having a phase over a subpulse width τ, where τ is a measure of time, and where the phase is based on the random subcode θ_(i); V) communicating the modulated subcode θ′_(i) to an antenna system; VI) receiving a time signal and using the time signal as the transmission time t_(i); IV) repeating step I), step II), and step III), step IV), step V), and step VI), thereby generating the plurality of random subcodes and communicating the plurality of phase conversion parameters; IIV) producing and providing a demodulated subcode θ_(R) by: IIV)A) receiving an echo return from the antenna system; IIV)B) demodulating the echo return and producing a demodulated subcode θ_(R); and IIV)C) providing the demodulated subcode θ_(R) to each range gate RG_(j) comprising the plurality of range gates RG_(j); and IIIV) processing the demodulated subcode θ_(R) by directing the each range gate to perform steps comprising: IIIV)A) receiving the demodulated subcode θ_(R); IIIV)B) identifying a most recent phase conversion parameter (ϕ_(k)−θ_(k)), where the most recent phase conversion parameter (ϕ_(k)−θ_(k)) is the phase conversion parameter (ϕ_(i)−θ_(i)) most recently provided to the each range gate RG_(j); IIIV)C) generating an echo subcode ϕ_(R) by converting the demodulated subcode θ_(R) using the most recent phase conversion parameter (ϕ_(k)−θ_(k)); IIIV)D) modifying a polyphase sequence comprising a string of subcodes by adding the echo subcode ϕ_(R) to the polyphase sequence, thereby generating an updated polyphase sequence; and IIIV)E) correlating the updated polyphase sequence using the set of polyphase subcodes having N number of members used by the polyphase subcode generator, thereby processing the demodulated subcode θ_(R), thereby processing echo returns; the antenna system in data communication with the one or more digital processors and the antenna system configured to receive the modulated subcode θ′_(i) and transmit the modulated subcode θ′_(i), in response to a transmit signal, and the antenna system configured to provide the echo return to the one or more digital processors; and a timing circuit in data communication with the antenna system and the one or more digital processors and configured to provide the time signal to the one or more digital processors and the transmit signal to the antenna system.
 17. The Continuous Wave Radar Apparatus of claim 16 where the one or more digital processors are further programmed to perform steps comprising: performing step IIV)A, step IIV)B), and step IIV)C over a period of time ΔT_(P); and providing the phase conversion parameter (ϕ_(i)−θ_(i)) to the each range gate RG_(j) using an associated D_(RG(j)) for the each range gate RG_(j), where the associated D_(RG(j)) for the each range gate RG_(j) is equal to 2τ(j)+ΔT_(P) and where 0.8≤D_(j)/D_(RG(j))≤1.2, where D_(j) is the delay D_(j) unique to the each range gate RG_(j), D_(RG(j)) is the associated D_(RG(j)) for the each range gate RG_(j), and ΔT_(P) is the period of time ΔT_(P).
 18. The Continuous Wave Radar Apparatus of claim 17 where the one or more digital processors are further programmed to direct the each range gate to correlate the updated polyphase sequence by using a matched filter comprising a reference register, where the reference register comprises the set of polyphase subcodes having N number of members used by the polyphase subcode generator.
 19. The Continuous Wave Radar Apparatus of claim 18 where the one or more digital processors are further programmed to: generate the phase conversion parameter (ϕ_(i)−θ_(i)) by performing operations equivalent to (ϕ_(i)−θ_(i))=f₁(ϕ_(i), θ_(i)) where f₁ is a mathematical function over at least some portion of a domain comprising ϕ_(i) and θ_(i), and where (ϕ_(i)−θ_(i)) is the phase conversion parameter (ϕ_(i)−θ_(i)), ϕ_(i) is the polyphase subcode ϕ_(i), and θ_(i) is the random subcode θ_(i); and direct the each range gate RG_(j) to generate the echo subcode ϕ_(R) by performing operations equivalent to ϕ_(R)=f₂((ϕ_(k)−θ_(k)), θ_(R)), where f₂ is a mathematical function over at least some portion of a domain comprising (ϕ_(k)−θ_(k)) and θ_(R) and where when 0.8≤θ_(i)/θ_(R)≤1.2 and 0.8≤(ϕ_(i)−θ_(i))/(ϕ_(k)−θ_(k))≤1.2, then 0.8≤ϕ_(i)/ϕ_(R)≤1.2, where θ_(R) is the demodulated subcode θ_(R), (ϕ_(k)−θ_(k)) is the most recent phase conversion parameter (ϕ_(k)−θ_(k)), and ϕ_(R) is the echo subcode ϕ_(R).
 20. The Continuous Wave Radar Apparatus of claim 19 further comprising a noise source in data communication with the one or more digital processors, and the one or more digital processors programmed to generate the random subcode θ_(i) using the noise source. 